New estimators based on order statistics in some families of scale distributions

In this study some new unbiased estimators based on order statistics are proposed for the scale parameter in some family of scale distributions. These new estimators are suitable for the cases of complete (uncensored) and symmetric doubly Type-II censored samples. Further, they can be adapted to Type II right or Type II left censored samples. In addition, unbiased standard deviation estimators of the proposed estimators are also given. Moreover, unlike BLU estimators based on order statistics, expectation and variance-covariance of relevant order statistics are not required in computing these new estimators.

Simulation studies are conducted to compare performances of the new estimators with their counterpart BLU estimators for small sample sizes. The simulation results show that most of the proposed estimators in general perform almost as good as the counterpart BLU estimators; even some of them are better than BLU in some cases. Furthermore, a real data set is used to illustrate the new estimators and the results obtained parallel with those of BLUE methods.